How do you solve trigonometry problems?

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Quick Answer

Successfully working through trigonometry problems requires knowledge of the properties of triangles as well as the ability to measure and understand the ratios called sine, cosine and tangent. Using equations associated with the ratios, it is possible to find the angles and lengths of right angle triangles.

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Trigonometry is not only useful in the classroom, but in the real world as well, such as in geosciences when measuring ocean waves and movements of tectonic plates. With a few basic guidelines in mind, solving trigonometry problems can be more simple than they appear.

Understanding ratios is the key to solving trigonometry problems involving right angles at 90 degrees. Use the ratios, sine = opposite side / hypotenuse; cosine = adjacent side / hypotenuse; and tangent = opposite side / adjacent. Depending on which two of the three variables you have, you can solve for the third using one of the three equations. This means that if you have two sides you can solve for an angle, you can also solve for a side length if you are given the value of an angle and the value of one of the sides. Working through these equations allows you to solve for all sides and angles. For accuracy, use a scientific calculator with the buttons "sin," "cos" and "tan."